   Chapter 19, Problem 71AP

Chapter
Section
Textbook Problem

Three long, parallel conductors carry currents of I = 2.0 A. Figure P19.71 is an end view of the conductors, with each current coming out of the page. Given that a = 1.0 cm, determine the magnitude and direction of the magnetic field at points A, B, and C. Figure P19.71

a)

To determine
The magnitude and direction of magnetic field at points A .

Explanation

Given info: The three conductors are parallel and carry equal currents of magnitude I=2.0A which is directed out of the page.

Explanation:

The arrangement of the wires is given by the following figure.

The magnetic field due to a straight current carrying wire is given by,

B=μ0I2πr       (1)

• μ0 is the permeability of free space
• I is the current in the wire
• r is the distance of the point from the wire

Let B1 be the magnitude of the magnetic field due to the conductor at point 1 , Let B2 be the magnitude of the magnetic field due to the conductor at point 2 , Let B3 be the magnitude of the magnetic field due to the conductor at point 3 .

At point A the B1 will be,

B1=μ0I2π(a2)

At point A the B2 will be,

B2=μ0I2π(a2)

At point A the B2 will be,

B3=μ0I2π(3a)

The horizontal component of B1 and B2 will cancel out each other, where as the vertical component of the magnetic field get added up. The magnetic field at A will have only vertical component and will be directed downward

b)

To determine
The magnitude and direction of magnetic field at points B .

c)

To determine
The magnitude and direction of magnetic field at point C .

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